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Chapter 4: Q. 37 (page 405)
The average value of the function on
The average value ofis
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If f is negative on [鈭�3, 2], is the definite integral positive or negative? What about the definite integral 鈭� ?
As n approaches infinity this sequence of partial sums could either converge meaning that the terms eventually approach some finite limit or it could diverge to infinity meaning that the terms eventually grow without bound. which do you think is the case here and why?
Compare the definitions of the definite and indefinite integrals. List at least three things that are different about these mathematical objects.
Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating
.
Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
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